How to Run Your First Quantum Circuit on a Free Cloud Simulator

The quickest free route is IBM Quantum Composer. Open it in a browser, place a Hadamard gate on one qubit, connect that qubit to a second with a controlled-NOT gate, measure both, and run the circuit on the simulator. The histogram should contain mostly 00 and 11 results. You do not need quantum hardware; a browser, notebook, or local simulator is enough.

What you are going to build

Your first circuit will be a two-qubit Bell-state circuit. IBM describes this as a circuit in which “two qubits become maximally entangled.” It is small enough to understand gate by gate, yet it demonstrates the ideas that make quantum computing different from ordinary bit manipulation: superposition, entanglement, measurement, repeated sampling, and statistical results.

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The circuit starts with both qubits in the state |0⟩. A Hadamard gate, written H, puts the first qubit into an equal superposition of 0 and 1. A controlled-NOT, or CNOT, flips the second qubit only when the first qubit is 1. Together, those operations create the state (|00⟩ + |11⟩) / √2. Measuring both qubits therefore produces matching values: 00 or 11. A single run is random, but many runs reveal the approximately even pattern.

A simulator calculates the circuit model in software and samples it repeatedly. It does not create a physical entangled pair, and it does not reproduce every imperfection of a real processor unless you deliberately add a noise model. That makes it ideal for learning circuit logic before you use scarce or billable hardware time.

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Run the Bell state in IBM Quantum Composer

Composer is the least complicated starting point because the circuit is assembled visually in a browser. IBM’s Composer documentation includes a guided first circuit, and IBM also documents a quickstart that builds and runs a circuit in under two minutes without a sign-in or API key. Interface labels can change, but the workflow remains the same.

1. Open IBM Quantum Composer. Start a new circuit and wait for the qubit wires and gate palette to appear.
2. Use two qubits. Keep the default two-wire layout if it is offered. The upper wire is conventionally called qubit 0 and the lower wire qubit 1.
3. Add a Hadamard gate. Place H on qubit 0 at the first time step. This creates the superposition needed for the Bell state.
4. Add a controlled-NOT. Place a CNOT with its control on qubit 0 and its target on qubit 1 at the next time step. The control and target must be in that direction; reversing them produces a different circuit.
5. Measure both qubits. Add measurement operations to qubit 0 and qubit 1. If Composer offers an automatic measurement control, use it; otherwise place one measurement on each wire.
6. Choose the simulator. Select the available simulator execution option rather than a physical quantum processor. For a first run, a few hundred or 1,000 shots is enough to see the distribution.
7. Run and inspect the histogram. Execute the circuit and open the result visualization. The two tall bars should correspond to 00 and 11; 01 and 10 should be absent or extremely rare in an ideal simulation.

If your first histogram is not exactly 50/50, that is normal. Each shot is a random sample from the Bell-state probabilities. With 100 shots, a result such as 47 instances of 00 and 53 of 11 is entirely plausible. Increasing the shot count makes the proportions tend toward one half, but it never makes an individual shot deterministic.

Understand every operation in the circuit

Initialization

Simulators normally initialize each qubit to |0⟩ unless you specify another state. In computational-basis notation, two initialized qubits are |00⟩. This is a starting condition, not a measurement result you have already observed.

Hadamard: creating a balanced choice

The Hadamard transforms |0⟩ into (|0⟩ + |1⟩) / √2. Before measurement, the qubit is described by amplitudes for both basis states. The simulator stores those amplitudes and calculates how later gates change them; it is not simply selecting a hidden classical 0 or 1.

CNOT: correlating the qubits

The CNOT leaves the target unchanged when the control is 0 and flips the target when the control is 1. Applied to the superposition created by the Hadamard, it maps the two branches to |00⟩ and |11⟩. The result is an entangled state: measuring one qubit predicts the other in the same measurement basis.

Measurement and shots

Measurement converts the quantum state into classical bit strings. A simulator run with 1,000 shots performs that sampling 1,000 times and reports counts. The counts are evidence of the probability distribution, not a list of 1,000 different quantum states that remain available after measurement.

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Free usage, accounts, and changing allowances

“Free” describes a current provider allowance, not a permanent promise that every simulator or processor is unlimited. Check the provider’s live terms before running large jobs, especially when a cloud account is attached to a billing profile.

You can complete the Bell-state exercise entirely locally or in a free notebook. A cloud account becomes relevant when you want managed execution, provider-specific simulators, job history, or a route toward real hardware.

Run the same circuit with Qiskit in Google Colab

Qiskit is the best next step when you want a reproducible script instead of a drag-and-drop circuit. IBM’s “Build and run your first quantum program” lesson is designed for a fresh Google Colab runtime. The lesson installs Qiskit, the Aer simulator package, and the IBM Runtime client, then lets you choose simulation rather than a real device.

Install the packages

In a new Colab cell, install the packages used by the lesson:

!pip install qiskit qiskit-aer qiskit-ibm-runtime

Restart the runtime only if Colab asks you to do so after installation. For a local-only Bell-state run, the IBM Runtime client is not required, but it is included in the lesson so that the same notebook can later be adapted for IBM services.

Create, simulate, and count results

from qiskit import QuantumCircuit
from qiskit_aer import AerSimulator

circuit = QuantumCircuit(2, 2)
circuit.h(0)
circuit.cx(0, 1)
circuit.measure([0, 1], [0, 1])

simulator = AerSimulator()
job = simulator.run(circuit, shots=1000)
result = job.result()
print(result.get_counts())

The output is a dictionary whose keys are measured bit strings and whose values are counts. You should see 00 and 11 with totals near 1,000 combined. Qiskit’s bit-string display convention can make the left-to-right order look reversed compared with the wire diagram because classical bit 0 is commonly printed on the right. If the counts are correct but the visual order surprises you, inspect the circuit’s qubit-to-classical-bit mapping rather than changing the gates.

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Make the result easier to interpret

Run the cell several times and compare the counts. The exact numbers change because the simulator samples randomly. Add a histogram in a later cell if you want a chart, but keep the raw count dictionary: it is the portable result that can be saved, tested, or compared with another simulator.

Run it with Amazon Braket

Amazon Braket gives you two distinct ways to simulate. The local simulator runs through the SDK without sending the circuit to a managed quantum device. Managed simulators run as AWS jobs and consume the applicable service allowance. AWS documents both a free local simulator and one hour of on-demand simulator time per month through the AWS Free Tier.

Use the local simulator

!pip install amazon-braket-sdk

from braket.circuits import Circuit
from braket.devices import LocalSimulator

circuit = Circuit().h(0).cnot(0, 1)
device = LocalSimulator()
result = device.run(circuit, shots=1000).result()
print(result.measurement_counts)

AWS’s Bell-state example uses the same gate sequence, Circuit().h(0).cnot(0,1). Its documented 1,000-shot example produced Counter({'11': 503, '00': 497}). Those exact counts are an illustration of sampling, not a required answer for your run.

Understand the SV1 option

AWS describes SV1 as an on-demand state-vector simulator for circuits up to 34 qubits. That capacity is a simulator specification, not a guarantee that every 34-qubit circuit will be fast or inexpensive: state-vector memory and runtime grow rapidly as qubits and operations increase. Use the local simulator for small experiments and reserve managed execution for jobs that need AWS-hosted infrastructure or a provider-specific workflow.

Protect an AWS account

Before submitting a managed job, verify the selected device, region, shot count, and current Free Tier status in the AWS console. Stop notebook runtimes and remove test resources when finished. The Free Tier allowance is monthly and conditional; do not treat it as an unlimited cloud budget.

Try Google Cirq in Colab

Cirq is a Python framework centered on circuit construction and simulation. Google’s setup tutorial uses Google Colab, which avoids a local Python installation for the first exercise.

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!pip install cirq

import cirq

q0, q1 = cirq.LineQubit.range(2)
circuit = cirq.Circuit(
    cirq.H(q0),
    cirq.CNOT(q0, q1),
    cirq.measure(q0, q1, key='result')
)

simulator = cirq.Simulator()
result = simulator.run(circuit, repetitions=1000)
print(result.histogram(key='result'))

The local Cirq simulator produces the same Bell-state pattern: matching outcomes dominate. Cirq’s tutorial also explains authentication for Quantum Engine access. That authentication is a separate step from running the local simulator; do not add cloud credentials merely to execute this notebook.

Choose the right beginner path

For a first success, use Composer. For repeatable experiments, use Qiskit, Braket, or Cirq in a notebook. The underlying Bell circuit is the same; the differences are setup, APIs, account handling, and how easily you can automate experiments.

Troubleshoot the first run

The histogram contains 01 or 10

• Check that the Hadamard is on qubit 0 and the CNOT control is also qubit 0.
• Confirm that the CNOT target is qubit 1, not another wire.
• Ensure both measurements occur after the gates, not before them.
• Inspect any circuit diagram or text representation for an accidental extra gate.

A tiny nonzero count can arise from a deliberately configured noise model, but an ideal simulator with the intended two-gate circuit should produce only the correlated strings.

The counts are not exactly equal

Increase the number of shots. A finite sample rarely divides perfectly in half. Compare the ratio, not whether the two numbers match digit for digit.

The notebook cannot import a package

• Run the installation cell in the same runtime that executes the circuit.
• Read the error for the package name: Qiskit’s simulator is supplied by qiskit-aer, while Cirq and Braket have their own packages.
• Restart the notebook runtime only when the environment requests it, then rerun the installation and import cells.
• Do not mix examples from different SDK versions without checking their current API names.

A managed cloud job asks for credentials or billing

Switch to the local simulator for the first lesson. A local run avoids provider authentication and demonstrates the same circuit logic. If you continue with managed execution, verify the account’s region, permissions, current free allowance, and billing settings before submitting jobs.

The simulator is slow or runs out of memory

Reduce the qubit count, circuit depth, or shot count. State-vector simulation stores amplitudes for every computational basis state, so the memory requirement grows exponentially with the number of qubits. A two-qubit Bell state is intentionally tiny; it does not imply that a simulator can handle an arbitrary large algorithm on a free notebook.

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Useful experiments after the Bell state

Change the measurement basis

Insert a Hadamard immediately before measuring a qubit and compare the histogram. You are no longer measuring the same observable as the original circuit, so the distribution changes even though the state-preparation gates are unchanged. This is a practical way to see that measurement basis matters.

Remove one gate at a time

Run three variants: only the Hadamard, only the CNOT applied to initialized qubits, and the complete circuit. The first shows a roughly even distribution on one qubit; the second has no effect when its control starts at 0; the complete circuit produces correlation. Keeping the shot count constant makes the comparison meaningful.

Add a third qubit carefully

Do not assume that adding a wire creates a three-qubit entangled state. Start by preparing the two-qubit Bell pair and leave the third qubit untouched, then measure all three. The third qubit should remain 0 while the first two match. This separates “more qubits” from “more entanglement.”

Compare simulators

Implement the same gate order in Composer, Qiskit, Braket, and Cirq. Record the shot count, bit-string convention, and result counts. Small differences in counts are sampling noise; systematic differences usually indicate a reversed control-target order, a different measurement mapping, or a different initial state.

When simulation is no longer enough

Simulation is the right tool for learning syntax, checking a circuit’s ideal behavior, and building intuition. A real quantum processor adds calibration drift, gate errors, readout errors, connectivity constraints, queue time, and device-specific compilation. Those effects can make 01 and 10 appear in a Bell-state histogram even when the ideal simulator never produces them.

Move to hardware only after the simulator result is understood and the circuit is saved in a reproducible form. Keep the original ideal counts as a baseline, document the device and date, and use the same shot count when comparing runs. Free access and queue availability change, so check the provider’s current terms immediately before submitting a hardware job.

Which option should you use?

Use IBM Quantum Composer if your priority is seeing a circuit and histogram with almost no setup. Use Qiskit if you want Python control and an easy path to scripted experiments. Use Amazon Braket if you already use AWS or want one SDK that distinguishes local simulation from managed devices. Use Cirq if its Python circuit model and Google-oriented workflow match your learning goals. All four can teach the same first lesson: a Hadamard followed by a CNOT creates correlated measurements, and repeated shots reveal probabilities rather than a single predetermined answer.

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Amazon Braketbeginner guideBell stateGoogle CirqIBM Quantum ComposerQiskitQuantum Computingquantum simulator